Ronald Dotzel

Abstract

Suppose G is a finite group
acting semifreely (i.e., free off the fixed set) on a finite CW complex X in the
homotopy type of Sn. When XG is also homotopy equivalent to Sn (as e.g., in
Sn× DK) necessary and sufficent conditions are given to determine the degree of
the inclusion XG→ X. It follows that for instance, if G is the group of
quaternions (nonabelian of order 8), the only attainable degrees are those ±1(mod8).